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Abstract

We propose a hybrid architecture for quantum information processing based on magnetically trapped ultracold atoms coupled via optical fields. The ultracold atoms, which can be either Bose-Einstein condensates or ensembles, are trapped in permanent magnetic traps and are placed in microcavities, connected by silica based waveguides on an atom chip structure. At each trapping center, the ultracold atoms form spin coherent states, serving as a quantum memory. An all-optical scheme is used to initialize, measure and perform a universal set of quantum gates on the single and two spin-coherent states where entanglement can be generated addressably between spatially separated trapped ultracold atoms. This allows for universal quantum operations on the spin coherent state quantum memories. We give detailed derivations of the composite cavity system mediated by a silica waveguide as well as the control scheme. Estimates for the necessary experimental conditions for a working hybrid device are given.

Figures (5)

Hybrid quantum processor using permanent magnetic traps and waveguides. (a) Sketch of the proposed device (not to scale) consisting of 1⃞ a substrate of permanent magnetic material, 2⃞ reflective coating on the edges, 3⃞ silica waveguides (vertical) for delivering the control/probe photons, 4⃞ an optical microcavity etched into a 5⃞ silica transparent substrate, 6⃞ a joint silica waveguide (horizontal) for transferring photons between nodes, 7⃞ a thermal phase-shifter and 8⃞ a micropattern into the magnetic material for creating the trapping magnetic fields. (b) Density plot of the simulated magnetic field local minima combined with a cross section of the optical microcavity and the silica waveguide.

(a) Single BEC qubit control. Two lasers are applied to the transitions between ground states and the excited states with transition energies ga and gb, and detuned each by an amount Δ. Spontaneous emission from the excited states to the ground states with decay rate Γ is present. (b) Rabi oscillations between levels a and b in the presence of spontaneous emission. The effective decoherence rate exp(−Γefft) is shown as the dotted line. (c) Initialization of SC qubits from various initial conditions: I. |1, 0〉〉, II.
|12,12〉〉. Parameters used are N = 1000, Δ/A = 1000, h̄Γ/A = 0.1, ga/A = 100, gb/A = 100 in (b) and gb/A = 0 in (c). The timescale is t0 = h̄/A.

Numerically simulated magnetic field local minima of a single trap created at a working distance of dmin ≈ 13.5μm with αh = 3μm, αs = 100μm and τ = 2μm. (a) Density plot of a confining magnetic field with a displaced optical axis of a cavity (small red circule). The magnetic field local minima is created with no external magnetic bias fields applied. (b) For the alignment purpose, the trap is displaced along the positive direction of the x-axis by applying an external magnetic bias field along the x-axis, such that By-bias = Bz-bias = 0 and Bx-bias = −1G. (c) The location of the magnetic trap is below the optical axis of the cavity with no external magnetic bias fields. (d) The magnetic trap is displaced along the z-axis to overlap with the optical axis of the cavity at dmin ≈ 16.0μm with external magnetic bias fields applied along the z-axis at Bx-bias = By-bias = 0 and Bz-bias = −1G.

(a) Scenarios for implementing the silica microcavity where Bragg mirrors are included in the design (2). (b) Possible implementations for the hybrid quantum device with a scheme to manipulate the traveling photons using the thermal phase shifters and entangling junctions (dotted line square). The connections in (b) are not to scale where the actual physical implementation would be modified accordingly to the experiment. The red circules represent the optical micro-cavities, the solid black lines are the silica waveguides and the yellow squares represent the thermal phase shifters which are used to modify the phase of the propagating photons to exclude particular targeted SC qubit(s) from being entangled.

The reflected power of the composite cavity system, two micro-cavities connected via a single silica waveguide. The simulation input parameters are
R1c=R2c=0.985,
R1wc=0.999,
R2wc=0.9 with both micro-cavities at equal lengths
L1,2c=30μm and the silica waveguide with a length of Lw = 4mm.